The equation of a circle $C$ is $x^2+y^2+16x+18y+144 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Solution: To find the equation in standard form, complete the square. $(x^2+16x) + (y^2+18y) = -144$ $(x^2+16x+64) + (y^2+18y+81) = -144 + 64 + 81$ $(x+8)^{2} + (y+9)^{2} = 1 = 1^2$ Thus, $(h, k) = (-8, -9)$ and $r = 1$.